Simplified Introduction of Cost-Volume-Profit Analyses Increases Understandability
Neal R. VanZante, Ph.D., CPA, CMA, CFM
Professor of Accounting
Texas A University-Kingsville

This paper demonstrates a simplified introduction of Cost-Volume-Profit (CVP) Analyses that the author uses in his classes before students read the textbook material covering the subject. The purposes of this introduction are to create interest in the subject and to simplify the computational aspects of CVP. As a first step, students are asked to look at the following income statement for the most recent year and predict next year's operating income assuming that the only change will be a 20% increase in sales volume.

Students are allowed a few minutes to work on the solution. As might be anticipated, student answers include 12, 16, and 30 representing 20% increases in operating income, gross margin, and revenue respectively. Normally, very few students recognize that there is not enough information to determine the correct answer. Because students typically have already been exposed to manufacturing accounting and to the variable/fixed cost relationships, the author quickly reminds them that Cost of Goods Sold and Operating Expenses may contain both variable and fixed costs.

Until the cost behavior has been properly analyzed, the new operating income cannot be predicted. Following a brief refresher of the definitions of variable and fixed costs, the next step is to provide the most recent income statement in the Contribution Margin format as follows:

Students are then asked to predict the operating income for next year, again assuming that the only change is a 20% increase in sales volume. Most students approach the problem by preparing a new income statement with 20% increases in the first three lines, no change in fixed costs, and determine the correct answer to be 18 as follows:

After the students have worked through the problem, the author demonstrates that the answer may be quickly calculated by adding 20% of the old Contribution Margin to the old Operating Income. Thus the new operating income could be calculated by adding 8 (20% of 40) to 10 giving 18. Additional discussion focuses on the various definitions of Contribution Margin and the fairly obvious idea that a change in Contribution Margin would change the Operating Income by an equal amount. Following a brief discussion of the definition of Break-even Point, students are asked to determine the Revenue necessary to achieve an operating income of zero. For simplicity, the original statement was deliberately set up so that percentages could be easily computed:

After giving the students a few minutes to work on the problem, the solution is provided by changing the Operating Income to zero and showing that the Contribution Margin would then need to be 30 as follows:

The above example is followed by a brief explanation that almost all problems dealing with determining the Break-even Point or Target Operating Income may be solved by calculating the Contribution Margin necessary to achieve the goal, then dividing by either the Contribution Margin Ratio or Contribution Margin Per Unit depending on whether the question calls for an answer in dollars or units.

Discussion then turns to the definition of the Margin of Safety and the Margin of Safety Ratio, which is 25% in the original problem. An alternative calculation of the Margin of Safety Ratio is shown as the Operating Income divided by the Contribution Margin (10/40=25%). Additional explanation of this alternative calculation is usually necessary, but students easily understand the logic. Namely, because Operating Income is increased by the same amount as the increase in Contribution Margin, then any amount of Contribution Margin exceeding the amount necessary to break-even would represent Operating Income. Thus, the percentage of Contribution Margin resulting in Operating Income must be equal to the percentage of Revenue in excess of Break-even Point.

Next, discussion turns to the definition of Operating Leverage. The original information is again offered as follows:

Students are shown that the Operating Leverage is calculated by dividing the Contribution Margin by the Operating Income (40/10), which provides an answer of 4. Several students normally observe that the Operating Leverage is the reciprocal of the Margin of Safety.

The author reminds students that the Operating Leverage is a measure of the effect on Operating Income given a change in Revenue Volume. Thus, if volume were expected to increase by 20%, then Operating Income would be expected to increase by 4 times 20% in our example. Of course, that means an increase in Operating Income of 80% would be expected. Students discover that in the original problem that the Operating Income did, in fact, increase by 80% (from 10 to 18). Usually, this point represents the end of the discussion for the class period. In later class periods, additional discussions and demonstrations of problem solving using simplified calculations are integrated with traditional solutions offered by solution manuals.

Depending upon the amount of time available and the course level, additional simplifications can be made for a variety of problems such as determining the number of units or sales prices necessary to achieve targeted operating income amounts or percentages. For example, assume that (in the original problem) the price per unit is 1 and we wish to determine the number of units necessary to achieve and operating income equal to 25% of revenue. The typical approach is to solve the following formula:

An easier approach is for students to recognize, by looking at the income statement, that the Contribution Margin is 40% of Revenue. So, if an Operating Income equal to 25% of Revenue is required, it follows that Fixed Costs must be equal to 15% of Revenue. Students quickly skip to the last part of the above calculation by simply dividing the Fixed Costs by 15 percent to derive 200 units.

An exercise or problem may require the student to calculate a sales price per unit necessary to achieve a certain operating income level. Assume that, given the original information, students are asked to determine the sales price necessary to achieve an Operating Income of 25% of Revenues without changing the number of units.

Assuming that the number of units will not change, then variable costs/expenses and fixed costs/expenses will not change. If Operating Income will equal 25% of Revenues, then 75% of Revenues will equal 90 (the total of variable and fixed costs/expenses. Revenue, then, is equal to 120 (90/.75), and sales price is 1.2 (120/100). Textbook approaches typically involve formulas similar to the one in the preceding example, but the last calculation is the same as shown here.

One may observe that the approaches demonstrated in this paper are simpler and faster ways to make the same calculations as is demonstrated in most textbooks. That, of course, is the point of the paper. The author's experience has been that student understanding is increased by presentation of these simplified approaches.